Résumé
Numerical Voronoi tessellation is used to investigate the mechanisms of frustration in some model glass systems. First, random packings of 8192 hard spheres of increasing volume fraction c are built using an efficient computer algorithm. Their Voronoi statistics evolves with c as if the system would like to reach a pure icosahedral order when extrapolating the volume fraction above the Bernal limit c(b) similar or equal to 0.645. Second, super-cooled liquid and glass samples of 1000 atoms are generated at different temperatures T after a quench from the liquid state, using classical micro-canonical molecular dynamics with a simple soft-sphere potential. When decreasing T, the ideal icosahedral order appears again as an extrapolated situation which cannot be realized due to geometrical frustration. Third, a model silica glass of 648 atoms is studied using the potential of van Beest, Kramer and van Santen and a quite similar quenching procedure is performed. As in the soft-sphere case the structural freezing following upon the glass transition is noticeable in all the geometrical characteristics of the Voronoi cells and again a possible interpretation in terms of geometrical frustration is proposed.